Do you have any other symptoms. What does your tongue look like? Is the phlegm thick or thin and does it have colour or is it clear? Why do you think there would be any kidney involvement?
Most of the time acute skin inflammation/redness is caused by damp heat. A wide variety of things affect that including your diet, stress levels, soaps/shampoos, makeup, the weather, and your activity level.
It could also just be a case of contact dermatitis. It would be better to have one of your fellow students or instructors needle you than needling yourself.
As for points, I’d use SJ 5 instead of SJ 2 or SJ 10. I’d probably also add GB 34 and LI 11 to clear damp heat and LU 6 (the xi-cleft of the lung helpful for acute conditions) and LU 7 to help with the phlegm.